An Addition Theorem and Some Product Formulas for q-Bessel Functions
Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1203-1221

Voir la notice de l'article provenant de la source Cambridge University Press

The most familiar series representation of the Bessel function is 1.1 Jackson [12] gave the following q-analogues: 1.2 1.3 where 0 < q < 1, the q-shifted factorials are defined by 1.4 and the q-gamma function is given by 1.5
Rahman, Mizan. An Addition Theorem and Some Product Formulas for q-Bessel Functions. Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1203-1221. doi: 10.4153/CJM-1988-051-7
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[1] 1. Askey, R., Beta integrals in Ramanujan's papers, his unpublished work and further examples, to appear. Google Scholar

[2] 2. Askey, R. and Ismail, M. E. H., A generalization of ultrasphericalpolynomials, in Studies in pure mathematics (Birkhauser-Verlag, Basel, 1983), 55–78. Google Scholar | DOI

[3] 3. Askey, R. and Roy, R., More q-beta integrals, Rocky Mountain J. Math. 16 (1986), 365–372. Google Scholar

[4] 4. Askey, R. and Wilson, J., Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985). Google Scholar

[5] 5. Carlitz, L., Some formulas of F. H. Jackson, Monatsh. fur Math. 73 (1969), 193–198. Google Scholar

[6] 6. Erdélyi, A., et al., ed., Higher transcendental functions, Vol. II (McGraw-Hill, New York, 1953). Google Scholar

[7] 7. Gasper, G. and Rahman, M., Positivity of the Poisson kernel for the continuous q-Jacobi polynomials and some quadratic transformation formulas for basic hypergeometric series, SIAM J. Math. Anal. 17 (1986), 970–999. Google Scholar

[8] 8. Gasper, G. and Rahman, M., Basic hypergeometric series (Cambridge University Press), to appear. Google Scholar

[9] 9. Hahn, W., Beitràge zur théorie der Heineschen Reichen, Math. Nachr. 2 (1949), 340–379. Google Scholar

[10] 10. Ismail, M. E. H., The basic Bessel functions and polynomials, SIAM J. Math. Anal. 12 (1981), 454–468. Google Scholar

[11] 11. Ismail, M. E. H., The zeros of basic Bessel functions, the functions J(x) and associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), 1–19. Google Scholar

[12] 12. Jackson, F. H., On generalized functions of Le gendre and Bessel, Trans. Roy. Soc. Edin. 41 (1903), 1–28. Google Scholar

[13] 13. Nassrallah, B. and Rahman, M., Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials, SIAM J. Math. Anal. 16 (1985), 186–197. Google Scholar

[14] 14. Rahman, M., Some infinite integrals of q-Bessel functions, to appear. Google Scholar

[15] 15. Rahman, M., An integral representation and some transformation properties of q-Bessel functions, J. Math. Anal. Appl. 125 (1987), 58–71. Google Scholar

[16] 16. Ramanujan, S., Notebook, Vols. I and II., Tata Institute of Fundamental Research, Bombay (1957). Google Scholar

[17] 17. Sears, D. B., Transformations of basic hypergeometric functions of special type, Proc. Lond. Math. Soc. (2), 52 (1951), 467–483. Google Scholar

[18] 18. Sears, D. B., On the transformation theory of basic hypergeometric functions, Proc. Lond. Math. Soc. 53 (1951), 158–180. Google Scholar

[19] 19. Slater, L. J., Generalized hypergeometric functions (Cambridge University Press, 1966). Google Scholar

[20] 20. Watson, G. N., A treatise on the theory of Bessel functions (Cambridge University Press, Paperback edition, 1966). Google Scholar

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